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- Title
A Roman Domination Chain.
- Authors
Chellali, Mustapha; Haynes, Teresa; Hedetniemi, Sandra; Hedetniemi, Stephen; McRae, Alice
- Abstract
For a graph $$G=(V,E)$$ , a Roman dominating function $$f:V\rightarrow \{0,1,2\}$$ has the property that every vertex $$v\in V$$ with $$f(v)=0$$ has a neighbor $$u$$ with $$f(u)=2$$ . The weight of a Roman dominating function $$f$$ is the sum $$f(V)=\sum \nolimits _{v\in V}f(v)$$ , and the minimum weight of a Roman dominating function on $$G$$ is the Roman domination number of $$G$$ . In this paper, we define the Roman independence number, the upper Roman domination number and the upper and lower Roman irredundance numbers, and then develop a Roman domination chain parallel to the well-known domination chain. We also develop sharpness, strictness and bounds for the Roman domination chain inequalities.
- Subjects
DOMINATING set; GRAPH theory; GEOMETRIC vertices; NUMBER theory; MATHEMATICAL bounds; MATHEMATICAL inequalities
- Publication
Graphs & Combinatorics, 2016, Vol 32, Issue 1, p79
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-015-1566-x